Application of the phase time and transmission coefficients to the study of transverse elastic waves in quasiperiodic systems with planar defects H. Aynaou a , V.R. Velasco b, * , A. Nougaoui a , E.H. El Boudouti a , B. Djafari-Rouhani c , D. Bria a a Laboratoire de Dynamique et d’Optique des Mat eriaux, D epartement de Physique, Facult e des Sciences, Universit e Mohamed Premier, 60000 Oujda, Morocco b Instituto de Ciencia de Materiales de Madrid, CSIC, Teora de la Materia Condensada, Cantoblanco, 28049 Madrid, Spain c Laboratoire de Dynamique et Structure des Mat eriaux Mol eculaires, U.R.A. CNRS 801, UFR de Physique, Universit e de Lille 1, F-59655 Villeneuve d’Ascq, France Received 27 February 2003; accepted for publication 9 May 2003 Abstract We study the transverse elastic waves in quasiperiodic structures by means of the transmission/reflection phase times and the corresponding transmission/reflection coefficients. We see that these concepts are powerful tools to study multilayer systems, besides the frequency spectrum. We study how the presence of planar defects in quasiperiodic Fibonacci and Rudin–Shapiro sequences strongly modify the phase times and transmission coefficient, and not only the frequency spectrum of the systems. Ó 2003 Elsevier Science B.V. All rights reserved. Keywords: Interface states; Surface defects; Surface waves 1. Introduction After the proposal of semiconductor superlat- tices [1] the study of the physical properties of multilayer systems has been very active. Besides the periodic multilayer systems, quasiperiodic systems have been also intensively studied [2,3]. Many theoretical studies based on simple 1D models have been performed, and interesting properties have been deduced [2,3]. The high level of control and perfection reached in the growth techniques of microstructures and nanostructureshasallowedtheproductionofsome quasiperiodic systems [4–9] by means of molecular beam epitaxy techniques. It should be stressed that the theory of all the mathematical and formal properties of quasiperiodic systems holds for infi- nitely large sequences, and this never happens in experiments or calculations. In practice we always deal with a ‘‘high’’ but finite realization. A finite realization is the n-generation which results from * Corresponding author. Tel.: +34-91-334-9045; fax: +34-91- 372-0623. E-mail address: vrvr@icmm.csic.es (V.R. Velasco). 0039-6028/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0039-6028(03)00695-2 Surface Science 538 (2003) 101–112 www.elsevier.com/locate/susc